Floor coverings do have an affect on radiant floors. Your system must be engineered to overcome any problems that floor coverings might have on heat output. A more important consideration, is the effect, that the heating system will have on the floor coverings.

Engineered Wood is Best for Radiant - Composed of three to five layers of wood glued together using cross-grain lamination, engineered wood flooring is more resistant to expansion and contraction due to temperature changes and moisture.
   Thinner than solid wood flooring, engineered wood are also more stable and dent-resistant. It can be installed over concrete subfloor, and above, below or on-grade. Engineered wood floors use floating, glue-down or staple-down methods, depending on the type of subflooring.
   Engineered wood flooring also offers better resistance to wearing, scratching and denting. Because it is made up of several layers, engineered floors can easily be sanded and re-sanded several times.

Hardwood And Radiant

If you're importing a tropical or exotic wood, you must pay close attention to the source and age of the wood as well as the method used in drying it. Quick drying creates stresses that can affect the wood later as it expands and contracts.
Which hardwood floors work best?  Extensive laboratory testing by Launstein Hardwood Floors in Mason, Mich., found that American hardwoods - including cherry, oak, ash, maple, hickory and walnut - are good choices for radiant-heat flooring.
For best results, use narrow boards, preferably not wider than 3 inches. Narrow boards will better accommodate wood's expansion and contraction across a floor.
Consider using quarter-sawn wood for planks wider than 3 inches, regardless of species, for enhanced dimensional stability.
The Launstein testing found that quarter-sawn planks up to 7 inches across (when properly installed) can work well with radiant heat systems.
The testing also found that hardwood flooring that is three-eighths of an inch thick conducts heat better than thicker floors and resists gapping.